imported>Dima Trushin: /* Exam */

2022-06-14T09:09:26Z

Exam

Новая страница

= Schedule =

* [https://zoom.us/j/93353235982?pwd=cmVUMDNWV1ExN3AxVXQ5djBqangrQT09 Lecture] Thursday 16:20–17:40

* [https://zoom.us/j/94362176506?pwd=RVNzM1JHbnVxdCs4L3Z1Y1NKeTJvdz09 Seminar 201] Thursday 18:10–19:30

= Teachers and assistants =

{| class="wikitable" style="text-align:center"
|-
! Группа !! 201 !! 202 !! 203 !! 204
|-
|| Lecturer ||colspan="4"| [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] [https://t.me/DimaTrushin Telegram]
|-
|| Teacher || [https://www.hse.ru/en/org/persons/209508745 Dima Trushin] || [https://www.hse.ru/org/persons/224875083 Andrew Mazhuga] || [https://www.hse.ru/en/org/persons/209813351 Nikita Medved] || [https://www.hse.ru/en/staff/kaleeva Galina Kaleeva]
|-
|| Assistant || [https://t.me/@xo_masha Masha Marchenko] || Daniil Kopytov || [https://t.me/johanddc/ Ваня Пешехонов] || [https://t.me/ivanovskayaaaaa Dasha Ivanova]
|}

= Consultations schedule =

{| class="wikitable"
|-
! !! Teacher/Assistant !! Monday !! Tuesday !! Wednesday !! Thursday !! Friday
|-
| <center>1</center> || Dima Trushin || || || [https://us04web.zoom.us/j/5515049969 zoom since 17:00] || ||
|-
| <center>2</center> || Andrew Mazhuga || || || || ||
|-
| <center>3</center> || Nikita Medved || || || write me in telegram https://t.me/medvednikita

and we will schedule a meeting
|| ||
|-
| <center>4</center> || Galina Kaleeva || || || 16.20-17.40.
Offline: S 913

Online: [https://us02web.zoom.us/j/88331684853?pwd=Uk9QZWYzOGtaZFBrZGFlMThXdDkzdz09 Zoom]

Passcode: algebra

In case I'm offline text me via [https://t.me/galinakaleeva telegram]
|| ||
|-
| <center>5</center> || Masha Marchenko || || || || ||
|-
| <center>6</center> || Daniil Kopytov || || || || ||
|-
| <center>7</center> || Vanya Peshekhonov || || || || [https://us04web.zoom.us/j/9906409936?pwd=dHMrVS9jU3FuTklWS1hQaUhRUC8rZz09 zoom] c 18:20 ||
|-
| <center>8</center> || Dasha Ivanova || || || || ||
|}

= Grading system =

The final grade is computed as follows

F = 0,3 * H + 0,3 T + 0,4 E

where H is the grade for the home assignments, T is the written test grade, and E is the final exam grade.

Only the final grade is rounded in the final formula according to the standard rule.

= Lecture abstracts =

'''Lecture 1''' (08.04.2021). Binary operations. Associativity, neutral element, inverse element, commutativity. Definition of a group. Additive and multiplicative notations. Subgroups and cyclic subgroups. The order of an element of a group.

'''Lecture 2''' (15.04.2021). Subgroups of the group of integers. Left and right cosets, examples. Normal subgroups. The Lagrange theorem.

'''Lecture 3''' (22.04.2021). Five corollaries of the Lagrange theorem. Homomorphisms and Isomorphisms of groups. Image and kernel of a homomorphism. Normal subgroups. Direct product of groups. Finite Abelian Groups. The Chinese Remainder Theorem. Structure of a finite abelian group.

'''Lecture 4''' (29.04.2021). Second version of the Chinese Remainder Theorem. Structure of Z_{p^n}^*. Cryptography. Exponentiation by squaring (fast raising to a power algorithm). The discrete logarithm problem. Diffie-Hellman key exchange.

'''Lecture 5''' (13.05.2021). Rings, commutative rings, fields, subrings. Invertible elements, zero divisors, nilpotent and idempotent elements. Ideals. Description of ideals in Z and Z_n. Homomorphisms and isomorphisms of rings. The Chinese remainder theorem for rings. The kernel and the image of a homomorphism, their properties.

'''Lecture 6''' (20.05.2021). Polynomials in one variable. Euclidean algorithm, greatest common divisor, ideals of F[x]. Irreducible polynomials and unique factorization of polynomials in F[x]. Ring of remainders, the Chinese Remainder Theorem for polynomials.

'''Lecture 7''' (27.05.2021). Characteristic of a field. Field extensions, an extension by a root. Finite fields: number of elements in a finite field, multiplicative group of a finite field is cyclic, classification of finite fields (without proof). How to produce finite fields. Galois random generator. Stream cipher.

'''Lecture 8''' (03.06.2021). Polynomials in several variables. Lexicographical orders, stabilization of strictly descending chains of monomials. An elementary reduction, a reduction with respect to a set of polynomials, remainders, Groebner basis. Stabilization of reduction.

'''Lecture 9''' (10.06.2021). S-polynomials and the Buchberger criterion. Ideals in a polynomial ring, the Buchberger algorithm to produce a Groebner basis of an ideal. A ring of remainders. Membership problem and variable elimination.

'''Lecture 10''' (17.06.2021). The Diamond Lemma. A proof of the Buchberger criterion.

= Problem sheets =

The solutions should be sent to your teaching assistant before the beginning of the next seminar.

'''Seminar 1''' (08.04.2021). [https://disk.yandex.ru/i/b3oiUcNp_rgiOA Problems]

'''Seminar 2''' (15.04.2021). [https://disk.yandex.ru/i/i7EhGprOjM9yFw Problems]

'''Seminar 3''' (22.04.2021). [https://disk.yandex.ru/i/druoZuJJTfUsLg Problems]

'''Seminar 4''' (29.04.2021). [https://disk.yandex.ru/i/ObhKt0v6Kj-d4A Problems]

'''Seminar 5''' (13.05.2021). [https://disk.yandex.ru/i/2cHws9wRUMkNoA Problems]

'''Seminar 6''' (20.05.2021). [https://disk.yandex.ru/i/P07PYPjuxnbX9A Problems]

Since Homework 6 is late, there is a special deadline for Group 201. The new deadline is Sunday 23:00 May 30. Deadlines for the other groups remain the same.

'''Seminar 7''' (27.05.2021). [https://disk.yandex.ru/i/v-gwT7_dvGvx2w Problems]

'''Seminar 8''' (03.06.2021). [https://disk.yandex.ru/i/e3OvTAA6MA0dOA Problems] Deadline for group 204: Friday, 18.06.2021, 14.40.

'''Seminar 9''' (10.06.2021). [https://disk.yandex.ru/i/AErL_P-U1FinzA Problems]

= Test =

Demo variant of the [https://disk.yandex.ru/i/GPUiapfVUdzc6g test]

= Exam =

* The [https://disk.yandex.ru/i/smwqxW5UXQxGBA link] to the rules and information regarding the exam.

= Results =

* Homework

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/11y6e-yqHgs12Qka_vdvR9NOUZiX9PmF1WrnP3HX6Uro/edit#gid=0 201] !! [https://docs.google.com/spreadsheets/d/11y6e-yqHgs12Qka_vdvR9NOUZiX9PmF1WrnP3HX6Uro/edit#gid=580483061 202] !! [https://docs.google.com/spreadsheets/d/11y6e-yqHgs12Qka_vdvR9NOUZiX9PmF1WrnP3HX6Uro/edit#gid=1410164784 203] !! [https://docs.google.com/spreadsheets/d/11y6e-yqHgs12Qka_vdvR9NOUZiX9PmF1WrnP3HX6Uro/edit#gid=133833186 204]
|}

* Summary Statement

{| class="wikitable" style="text-align:center"
|-
! [https://docs.google.com/spreadsheets/d/1qIcyiaujcd8DCYoClJQ70dqbZHIONdM4j1ERpTJgL84/edit#gid=0 201] !! [https://docs.google.com/spreadsheets/d/1qIcyiaujcd8DCYoClJQ70dqbZHIONdM4j1ERpTJgL84/edit#gid=312933063 202] !! [https://docs.google.com/spreadsheets/d/1qIcyiaujcd8DCYoClJQ70dqbZHIONdM4j1ERpTJgL84/edit#gid=1854307677 203] !! [https://docs.google.com/spreadsheets/d/1qIcyiaujcd8DCYoClJQ70dqbZHIONdM4j1ERpTJgL84/edit#gid=1284918112 204]
|}

= Links =

* [https://disk.yandex.ru/d/qpt65RyLytBMCw?w=1 '''Lecture Notes''']

* [https://disk.yandex.ru/d/Bk0bacA5HuxA8w?w=1 '''Seminars 201''']

* Two seminars 203 online: [https://youtu.be/lhR08fZbDy0 '''8'''], [https://youtu.be/OTR6Y2hLlCY '''9'''] and corresponding whiteboards: [https://miro.com/app/board/o9J_l__r74c=/ '''8'''], [https://miro.com/app/board/o9J_l_YHP9Y=/ '''9''']

Algebra DSBA 2020/2021 - История изменений

imported>Dima Trushin: /* Exam */